"We need to support Aung San Suu Kyi and her leadership but also be very clear and unequivocal to the military power sharing in that government that this is unacceptable", Tillerson said.
"United Nations Security Council resolutions, including the most recent unanimous sanctions resolution, represent the floor, not the ceiling, of the actions we should take".
Mr Tillerson visited No 10 for detailed talks with the UK National Security Adviser Mark Sedwill today before a broader meeting with Foreign Secretary Boris Johnson.
"The prime minister underlying its importance in preventing Iran from procuring nuclear weapons", May's spokesman said.
The U.N.'s International Atomic Energy Agency claims Iran has met its obligations so far under the 2015 accord.
Mr Tillerson said he discussed with Mrs May "the threat that Iran poses to the region through its destabilising activities in Yemen, in Syria and in other parts of the region".
N.Korea condemns Tokyo, Seoul over latest United Nations sanctions
Shortly after, Japan's Chief Cabinet Secretary Yoshihide Suga denounced Pyongyang's comments as "extremely provocative". While the latest sanctions are not as tough as what the USA had sought, they are expected to have a significant impact.
'They agreed on the importance of the global community continuing to work together to put pressure on the regime'.
Mr Tillerson praised the co-operation between the UK, US and France in dealing with the aftermath of Hurricane Irma in the Caribbean.
The U.S. pushed for an oil embargo as part of a resolution at the UN Security Council after North Korea conducted its sixth nuclear test on September third but failed to get it adopted in the face of resistance from China and Russian Federation.
The Foreign Secretary will also chair a meeting on Libya with the Special Representative of the United Nations Secretary General for Libya, Ghassan Salamé, US Secretary of State Tillerson, Italian Foreign Minister Angelino Alfano, Egyptian Foreign Minister Sameh Shoukry, United Arab Emirates Minister of State for Foreign Affairs, Dr Anwar bin Mohamed Gargash and the French Political Director Nicolas de Rivière. "Close coordination with our allies is vital for both the short-term and long-term recovery efforts", Johnson was quoted as saying Wednesday ahead of the meeting.
"Helping to bring stability to Libya is a vital part of United Kingdom efforts to tackle the threat from terrorism and the issue of illegal migration, which exist in close proximity to Europe", the Foreign Office said.
'Britain will continue to work closely alongside our partners to tackle the shared challenges we face worldwide'.